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USER GUIDE
Texas Instrument BA II Plus Calculator
April 2007
GENERAL INFORMATION
The Texas Instrument BA II Plus financial calculator was designed to support the many possible
applications in the areas of financial analysis and banking.
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The explanations below will make it easier for you to use the calculator.
‰
By default, the calculator operates in financial mode.
‰
The ON/OFF key is used to turn the calculator on and off.
‰
The 2ND key is often used to access financial applications. Press this key when you
want to apply the functions displayed in yellow at the top of the keys.
‰
The FORMAT feature lets you select the number of decimal points to be displayed by the
calculator. If you want to display:
¾
a fixed decimal point, press 2ND and then FORMAT, enter a number from 0 to 8
to specify the number of decimal points, and then press ENTER.
¾
a floating decimal point, press 2ND and then FORMAT, enter the number 9, and
then press ENTER. The number of decimals displayed will vary depending on the
calculations up to a maximum of nine decimals.
To perform the calculator exercises in this document, it is best to use a floating decimal
point format.
‰
Setting the number of payment periods and interest-calculation periods in a financial
calculation (the P/Y and C/Y functions).
¾
P/Y function: this function sets the number of annual payments. The default value
is one payment per year. To change the number of annual payments, press the
2ND and P/Y keys, enter the required value, and then press ENTER (for
example, 12 for 12 monthly payments).
¾
C/Y function: this function sets the number of interest-calculation periods. By
default, the number of interest-calculation periods is the same as the number
entered for the P/Y variable. To change it, press 2ND, P/Y and È, and then enter
the number of periods and press ENTER.
Example where the C/Y differs from the P/Y: monthly payments on a personal loan on
which interest is calculated quarterly (I, 4):
Sequence of entries
Display
Explanation
2ND > P/Y > 12 > ENTER
P/Y = 12
Enters a monthly payment
period (12 months).
2ND > P/Y > È > 4 >
ENTER
C/Y = 4
Enters a quarterly interestcalculation period (4 threemonth periods per year).
N. B.: It is important to follow the sequence of entries without pressing any other key.
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‰
The BGN function lets you activate the beginning-of-period or the end-of-period payment.
To understand the configuration of this function, simply press the 2ND and BGN keys. To
the left of your screen, you will then see the END or BGN letters.
To activate the beginning-of-period payment calculation, simply press the 2ND, BGN,
2ND and SET keys. The BGN indicator then appears in the upper-right area of the
display screen. To return to END, simply repeat the 2ND, BGN, 2ND and SET sequence:
the BGN indicator will disappear.
‰
The CE/C key clears the on-screen data without deleting any numerical values that have
been entered.
‰
The CLR TVM function cancels the numeric values and calculation commands and
resets the calculator’s default financial values. Before performing each calculation, users
are advised to cancel all previously used numerical values by pressing the 2ND and CLR
TVM keys.
These keys, however, do not affect the beginning-of-year payment (BGN) mode or endof-period payment (END) mode or the values attributed to P/Y and C/Y. Therefore, it is
important to make sure that these values have been programmed before performing a
calculation.
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FINANCIAL CALCULATIONS
Most financial calculations are carried out using the following seven keys:
Financial keys
These keys are used to designate or calculate:
N
The number of periods.
I/Y
The nominal interest rate.
PV
The present value of an investment.
FV
The future value of an investment.
PMT
The periodic payment of an amortized loan or a split
annuity.
CPT
Compute key.
BGN
Indicates whether the calculations include the payments
made at the beginning or at the end of each period.
Note:
By convention, the present value of an investment is a negative value. The calculator is
programmed this way; therefore, in calculations of future values or per-period payments, if the
present value is entered as a negative value, the future value or the value of the payments will
be positive. The opposite is also true. It is therefore important to be thorough and refer to the
calculator’s user guide, if necessary.
Sample calculation of the future value (FV) of a single payment
Someone wishes to invest $4,000 in a registered retirement savings plan (RRSP) for a five-year
period.
Insurer A proposes an annual compound interest rate of 6%, whereas insurer B proposes a
nominal rate of 5.95% compounded on a semi-annual basis. The following two tables should
help you determine which insurer is proposing the best investment.
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Insurer A
Sequence of entries
Display
Explanation
CE/C > 2ND > CLR TVM
0
2ND > P/Y > 1 > ENTER
P/Y = 1
Enters an annual payment period.
0
Exits the entry of the P/Y variable.
CE/C > CE/C
Resets the default values.
5>N
N=5
Enters a five-year period.
6 > I/Y
I/Y = 6
Enters an annual interest rate of 6%.
4,000 > +/− > PV
CPT > FV
PV = − 4,000
Enters the present value of the
investment.
FV = 5,352.90231
Calculates the final value of the
investment.
Insurer B
Sequence of entries
Display
CE/C > 2ND > CLR TVM
0
2ND > P/Y > 2 > ENTER
P/Y = 2
CE/C > CE/C
5 > 2ND > xP/Y > N
5.95 > I/Y
4,000 > +/− > PV
CPT > FV
0
N = 10
I/Y = 5.95
PV = − 4,000
FV = 5,362.632027
Explanation
Resets the default values.
Enters a semi-annual payment period.
Exits the entry of the P/Y variable.
Enters the number of periods over five
years.
Enters a nominal interest rate of 5.95%.
Enters the present value of the investment.
Calculates the final value of the
investment.
The investment proposed by Insurer B returns a greater cumulative value, after five years, of
approximately $9.73.
Calculating the future value of an annuity
A client would like to invest $2,500 per year over the next five years. He would like to know what
the cumulative value of the investment would be in five years if the annual realized rate were 5%
in a situation where the investment is made at the beginning of the year and in a situation where
the investment is made at the end of the year.
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¾
$2,500 investment made at the beginning of the year
Sequence of entries
CE/C > 2ND > CLR TVM
2ND > BGN > 2ND >
SET
2ND > P/Y > 1 > ENTER
CE/C > CE/C
2,500 > +/− > PMT
Display
0
BGN
Explanation
Resets the default values.
Activates the calculation of beginning-ofperiod payments.
P/Y = 1
Enters an annual payment period.
0
Exits the entry of the P/Y variable.
PMT = − 2,500
Enters the amount of the annual
investment.
5>N
N=5
Enters the number of periods.
5 > I/Y
I/Y = 5
Enters the annual interest rate.
CPT > FV
¾
FV = 14,504.78203
Calculates the cumulative value of the
annuity.
$2,500 investment made at the end of the year
Sequence of entries
Display
CE/C > 2ND > CLR TVM
0
2ND > BGN > 2nd > SET
END
2ND > P/Y > 1 > ENTER
P/Y = 1
Enters an annual payment period.
0
Exits the entry of the P/Y variable.
CE/C > CE/C
2,500 > +/− > PMT
PMT = − 2,500
Explanation
Resets the default values.
Activates the calculation of end-of-period
payments.
Enters the amount of the annual
investment.
5>N
N=5
Enters the number of periods.
5 > I/Y
I/Y = 5
Enters the annual interest rate.
CPT> FV
FV = 13,814.07812
Calculates the cumulative value of the
annuity.
Obviously, an investment made at the beginning of the year will result in a higher cumulative
value (other variables being equal), as the interest will begin to accumulate on the very first day.
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Calculating the payment of a personal or mortgage loan
The process of calculating a personal or mortgage loan consists of:
‰
Determining the known variables;
‰
Entering the number of payment periods (P/Y) and the number of interest-calculation
periods (C/Y);
‰
Calculating the unknown variable.
Sample calculation of a personal loan repayment
Mary wants to borrow $15,000 to purchase a new car, and she wants to repay the loan over a
five-year period. If the bank demands a nominal rate of 6% compounded on a monthly basis,
what would be the monthly repayment (end of period)?
Known variables:
- nominal rate: (6%,12)
- term of the loan: five years (60 monthly payments)
- capital borrowed: $15,000
- Number of annual payments: 12
- Number of interest-calculation periods: 12
The monthly repayment can be calculated using the following operations:
Sequence of entries
Display
Explanation
CE/C > 2ND > CLR TVM
0
2ND > P/Y > 12 > ENTER
P/Y = 12
Enters a monthly payment period.
0
Exits the entry of the P/Y variable.
CE/C > CE/C
Resets the default values.
5 > 2ND > xP/Y > N
N = 60
Enters the number of monthly payments
over five years.
6 > I/Y
I/Y = 6
Enters the nominal interest rate.
15,000 > +/− > PV
CPT > PMT
PV = − 15,000
PMT = 289.9920229
Enters the amount of the loan.
Calculates the amount of the monthly
payments.
To repay this loan over a five-year period, the monthly repayment amount would be $289.99.
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Sample calculation of a mortgage loan repayment
Claude buys a home for $125,000 and makes a $40,000 cash downpayment. To finance the
balance, the bank offers him an $85,000 mortgage loan at a nominal rate of 6% compounded on
a semi-annual basis.
What monthly payments will be required to repay this mortgage over a 20-year term?
What will the mortgage balance be after five years?
To answer these two questions, the known variables must first be determined:
- nominal rate: (6%, 2)
- term of the loan: 20 years (240 monthly payments)
- capital borrowed: $85,000
The monthly mortgage repayment can be calculated using the following operations:
Sequence of entries
CE/C > 2ND > CLR
TVM
Display
0
Explanation
Resets the default values.
2ND > P/Y > 12 >
ENTER
P/Y = 12
Enters a monthly payment period.
È > 2 > ENTER
C/Y = 2
Enters a semi-annual interestcalculation period.
CE/C > CE/C
20 > 2ND > xP/Y > N
6 > I/Y
85,000 > +/− > PV
CPT > PMT
0
Exits the entry of the C/Y variable.
N = 240
Enters the number of monthly
payments over a 20-year period.
I/Y = 6
Enters the nominal interest rate.
PV = − 85,000
PMT = 605.3601756
Enters the loan amount.
Calculates the monthly repayment
amount.
To repay this loan over a 20-year period, the monthly repayment amount would be $605.36.
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The balance of the mortgage loan after five years is calculated using the following operations,
after having computed the monthly payment of $605.36:
Sequence of entries
Display
Explanation
Do not change the data already entered for the financial variables
5 > 2ND > xP/Y > N
CPT > FV
N = 60
FV = 72,076,74454
Enters the number of monthly
payments over a five-year period.
Calculates the loan balance after 60
monthly payments.
The balance of the mortgage loan after five years is therefore $72,076.74.
In financial mathematics, it is often a good idea to double-check calculations. In this example,
another way to calculate the mortgage balance after 5 years would be to calculate the
present value of monthly payments of $605.36 over 15 years, i.e., the remaining term of the
loan.
The balance of the mortgage loan after five years can be calculated using the following
operations:
Sequence of entries
Display
CE/C > 2ND > CLR TVM
0
Explanation
Resets the default values.
2ND > P/Y > 12 >
ENTER
P/Y = 12
Enters a monthly payment period.
È > 2 > ENTER
C/Y = 2
Enters a semi-annual interestcalculation period.
CE/C > CE/C
15 > 2ND > xP/Y > N
6 > I/Y
0
N = 180
Exits the entry of the C/Y variable.
Enters the number of monthly
payments for the 15 remaining
years.
I/Y = 6
Enters the nominal interest rate.
605.3601756 > PMT
PMT = 605.3601756
Enters the amount of the monthly
payments.
CPT > PV
PV = −72,076.74454
Calculates the loan balance after 60
monthly payments.
The balance of the mortgage loan after five years is therefore $72,076.74.
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Self-Evaluation Exercise
Question 1.
You borrow $75,000 to buy a house and agree to repay the loan in 20 years at
an interest rate of (6.5%, 2). How much lower would your monthly payment be
with a (6%, 2) interest rate?
a) $555.38
b) $534.15
c) $21.24
d) $24.21
e) $34.24
Question 2.
What nominal rate, compounded semi-annually, lets you double your capital in
ten years (rounded off)?
a) 6%
b) 7%
c) 8%
d) 9%
e) 10%
Question 3.
You are thinking about purchasing a $10,000 bond maturing at par in nine
years with annual coupons at the rate of 7%. How much will you have to pay if
you want a compound annual return of 8%?
a) $4,372.82
b) $9,002.49
c) $9,375.31
d) $10,000.00
e) $10,375.31
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Question 4.
What will your mortgage loan balance be after four years if the following
conditions apply (round off to the nearest dollar)?
Amount of the loan: $110,000
Interest rate: (8%, 2)
Term of the loan: 25 years with monthly repayments
a) $103,361
b) $93,360
c) $83,953
d) $98,360
e) $100,630
Question 5.
What is the cumulative value after seven years of a monthly investment of
$500 (made at the end of each month) if the nominal rate is (9%, 12) (round off
to the nearest dollar)?
a) $48,213
b) $43,000
c) $53,000
d) $55,813
e) $58,213
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Answer Sheet
Answer 1.
You borrow $75,000 to buy a house and agree to repay the loan in 20 years at
an interest rate of (6.5%, 2). How much lower would your monthly payment be
with an interest rate of (6%, 2)?
a) $555.38
b) $534.15
c) $21.24
d) $24.21
e) $34.24
The correct answer is c).
Reason:
Sequence of entries
Display
Explanation
CE/C > 2ND > CLR TVM
0
Resets the default values.
2ND > P/Y > 12 > ENTER
P/Y = 12
Enters a monthly payment
period.
È > 2 > ENTER
C/Y = 2
Enters a semi-annual interestcalculation period.
CE/C > CE/C
75,000 > +/− > PV
0
Exits the entry of the C/Y
variable.
PV = − 75,000
Enters the loan amount.
6.5 > I/Y
I/Y = 6.5
Enters the nominal interest rate.
20 > 2ND > xP/Y > N
N = 240
Enters the number of monthly
payments over a 20-year period.
CPT > PMT
PMT = 555.3753129
Calculates the amount of the
monthly payment.
Do not clear the values of the financial variables
6 > I/Y
CPT > PMT
I/Y = 6
PMT = 534.1413314
Enters the second nominal
interest rate.
Calculates the amount of the
monthly payment.
Therefore, $555.38 − $534.14 = $21.24
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Answer 2. What nominal rate, compounded semi-annually, lets you double your capital in
ten years (rounded off)?
a) 6%
b) 7%
c) 8%
d) 9%
e) 10%
The correct answer is b).
Reason:
Sequence of entries
Display
CE/C > 2ND > CLR TVM
0
2ND > P/Y > 2 > ENTER
P/Y = 2
CE/C > CE/C
0
10 > 2ND > xP/Y > N
1,000 > +/− > PV
Explanation
Resets the default values.
Enters a semi-annual payment
period.
Exits the entry of the C/Y
variable.
N = 20
Enters the number of monthly
payments over a 10-year
period.
PV = − 1,000
Enters the present value of the
investment.
2,000 > FV
FV = 2,000
Enters the final value of the
investment.
CPT > I/Y
I/Y = 7.052984768
Calculates the semi-annual
interest rate.
Note: The values of $1,000 and $2,000 were chosen arbitrarily. Any value and double that
amount would have given the same answer.
Answer 3.
You are thinking about purchasing a $10,000 bond maturing at par in nine years
with annual coupons at the rate of 7%. How much will you have to pay if you
want a compound annual return of 8%?
a) $4,372.82
b) $9,002.49
c) $9,375.31
d) $10,000.00
e) $10,375.31
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The correct answer is c).
Reason:
Sequence of entries
Display
Explanation
CE/C > 2ND > CLR TVM
0
2ND > P/Y > 1 > ENTER
P/Y = 1
Enters an annual payment period.
CE/C > CE/C
0
Exits the entry of the C/Y variable.
10 000 > FV
FV = 10 000
Enters the value of the bond at
maturity.
9>N
N=9
Enters the number of periods.
8 > I/Y
I/Y = 8
Enters the annual interest rate.
PV = −5,002.489671
Calculates the present value of
the bond.
CPT > PV
CE/C > 2ND > CLR TVM
0
700 > PMT
PMT = 700
Resets the default values.
Resets the default values.
Enters the value of a coupon (7%
× $10,000).
8 > I/Y
I/Y = 8
Enters the annual interest rate.
9>N
N=9
Enters the number of periods.
PV = − 4,372.821538
Calculates the present value of
interest coupons.
CPT > PV
Therefore, the amount payable is $5,002.49 + $4,372.82 = $9,375.31.
Answer 4.
What will your mortgage loan balance be after four years if the following
conditions apply (round off to the nearest dollar)?
Amount of the loan: $110,000
Interest rate: (8%, 2)
Term: 25 years with monthly repayments
a) $103,361
b) $93,360
c) $83,953
d) $98,360
e) $100,630
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The correct answer is a).
Reason:
Sequence of entries
CE/C > 2ND > CLR TVM
Display
0
Explanation
Resets the default values.
2ND > P/Y > 12 >
ENTER
P/Y = 12
Enters a monthly payment period.
È > 2 > ENTER
C/Y = 2
Enters a semi-annual interestcalculation period.
CE/C > CE/C
0
25 > 2ND > xP/Y > N
8 > I/Y
110,000 > +/− > PV
CPT > PMT
Exits the entry of the C/Y variable.
N = 300
Enters the number of monthly
payments over a 25-year period.
I/Y = 8
Enters the nominal interest rate.
PV = − 110,000
PMT = 839.5348005
Enters the loan amount.
Calculates the amount of monthly
payments.
After four years: Do not clear the values of the financial variables
21 > 2ND > xP/Y > N
N = 252
PV = − 103,360.9468
CPT > PV
Enters the number of monthly
payments over 21 years.
Calculates the loan balance after 48
monthly payments.
The mortgage balance after four years is $103,361.
Answer 5.
What is the cumulative value after seven years of a monthly investment of $500
(made at the end of each month) if the nominal rate is (9%, 12) (round off to the
nearest dollar)?
a) $48,213
b) $43,000
c) $53,000
d) $55,813
e) $58,213
The correct answer is e).
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Reason:
Sequence of entries
Display
Explanation
CE/C > 2ND > CLR TVM
0
2ND > P/Y > 12 > ENTER
P/Y = 12
Enters a monthly payment period.
0
Exits the entry of the P/Y variable.
CE/C > CE/C
Resets the default values.
7 > 2ND > xP/Y > n
N = 84
Enters the number of monthly payments
over seven years.
9 > I/Y
I/Y = 9
Enters the nominal interest rate.
PMT = − 500
Enters the amount of the monthly
investment.
500 > +/− > PMT
CPT > FV
FV = 58,213.46422
Calculates the cumulative value after
seven years.
The cumulative value after seven years is $58,213.
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